{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QAHT6ASGQ4COCE5LQBDBSLMG57","short_pith_number":"pith:QAHT6ASG","schema_version":"1.0","canonical_sha256":"800f3f02468704e113ab8046192d86efde1c1ff87e3fd5302f434d2d8f9dd665","source":{"kind":"arxiv","id":"0902.3833","version":5},"attestation_state":"computed","paper":{"title":"Towards a gauge theory for evolution equations on vector-valued spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Delio Mugnolo, Stefano Cardanobile","submitted_at":"2009-02-23T01:05:37Z","abstract_excerpt":"We investigate symmetry properties of vector-valued diffusion and Schr\\\"odinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\\Omega, H)$ that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0902.3833","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-23T01:05:37Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"f5c910e38da469e0631b03cfe8803b35335817ff0476678d9efa3aea2e29f29d","abstract_canon_sha256":"1363e8cf732d0d9da9d75a8b271bb317091c304dcb9e99e56a47d9eb9965bef4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:23.161179Z","signature_b64":"IHOdzAazUkJkbu/ERFmCGAl0b00q/QPsYNjlwhp8xsTyEcCrHdnNbD/Y1SEsh5ZmDSeV0ULCnSbHYFeWEyp6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"800f3f02468704e113ab8046192d86efde1c1ff87e3fd5302f434d2d8f9dd665","last_reissued_at":"2026-05-18T04:16:23.160691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:23.160691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a gauge theory for evolution equations on vector-valued spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Delio Mugnolo, Stefano Cardanobile","submitted_at":"2009-02-23T01:05:37Z","abstract_excerpt":"We investigate symmetry properties of vector-valued diffusion and Schr\\\"odinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\\Omega, H)$ that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3833","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0902.3833","created_at":"2026-05-18T04:16:23.160771+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.3833v5","created_at":"2026-05-18T04:16:23.160771+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3833","created_at":"2026-05-18T04:16:23.160771+00:00"},{"alias_kind":"pith_short_12","alias_value":"QAHT6ASGQ4CO","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QAHT6ASGQ4COCE5L","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QAHT6ASG","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57","json":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57.json","graph_json":"https://pith.science/api/pith-number/QAHT6ASGQ4COCE5LQBDBSLMG57/graph.json","events_json":"https://pith.science/api/pith-number/QAHT6ASGQ4COCE5LQBDBSLMG57/events.json","paper":"https://pith.science/paper/QAHT6ASG"},"agent_actions":{"view_html":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57","download_json":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57.json","view_paper":"https://pith.science/paper/QAHT6ASG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.3833&json=true","fetch_graph":"https://pith.science/api/pith-number/QAHT6ASGQ4COCE5LQBDBSLMG57/graph.json","fetch_events":"https://pith.science/api/pith-number/QAHT6ASGQ4COCE5LQBDBSLMG57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57/action/storage_attestation","attest_author":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57/action/author_attestation","sign_citation":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57/action/citation_signature","submit_replication":"https://pith.science/pith/QAHT6ASGQ4COCE5LQBDBSLMG57/action/replication_record"}},"created_at":"2026-05-18T04:16:23.160771+00:00","updated_at":"2026-05-18T04:16:23.160771+00:00"}